If a function f, defined f(g)=g^-1 maps a group G to G, is isomorphic, then G is abelian. How do I go about proving this one?
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Let $\displaystyle a,b\in G$, then $\displaystyle ab=f((ab)^{-1})=f(b^{-1}a^{-1})=f(b^{-1})f(a^{-1})=ba$ thus G is abelian
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